Method and system for measuring the angular velocity of a body orbiting in space

Abstract

The invention relates to a method for measuring the angular velocity ({right arrow over (ω)}) of a body ( 2 ) orbiting, or in motion anyway, in space depending on the detection of the trajectory of a plurality (n) of feature points (Pi) to be observed of said body ( 2 ), said trajectory being detected on the basis of data acquired by at least one remote sensor ( 1 ); the invention relate also to the related system for measuring the angular velocity ({right arrow over (ω)}) of a body ( 2 ) orbiting, or in motion anyway, in space using such method and that comprises at least one remote sensor ( 1 ), it being possible for said at least one sensor ( 1 ) to be installed on board a spacecraft ( 3 ) or to be housed in a earth station ( 5 ). The present invention has a preferred application for measuring the angular velocity in fields such as for recovering and de-orbiting space debris.

1 . A method for measuring the angular velocity ({right arrow over (ω)}) of a body ( 2 ) orbiting in space, comprising the following steps:
 n. preparing at least one remote sensor ( 1 ) (step  101 ); 
 o. defining a plurality (n) of feature points (Pi) to be observed of said body ( 2 ) orbiting in space (step  102 ); 
 p. acquiring, by the at least one remote sensor ( 1 ), data relevant to the positions taken over time (Pi(tk)) by the observed feature points (Pi) of said body ( 2 ) (step  103 ); 
 q. taking into account said plurality (n) of feature points (Pi), identifying 
 
       
         
           
             
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       triads of said points (Pi), to which just as many triads (Aj) of axes correspond (step  104 );
 r. identifying a triad of axes (Aj(tk)) associated to the first three points (Pu(tk),Pv(tk),Pw(tk) with u≠v≠w) available for each k th  instant (step  105 ); 
 s. for each k th  instant, evaluating the quaternions (qj(tk)) describing the orientation of the triad (Aj(tk)), associated to the triad (Pu(tk),Pv(tk),Pw(tk)), with respect to an inertial reference frame (step  106 ); 
 t. selecting a particular triad of axes (A*) and evaluating the quaternions (q*(tk)) describing its orientation with respect to said inertial reference frame depending on the quaternions (qj(tk)) identified in the previous step  106  (step  107 ); 
 u. estimating the quaternions (q*(tk)) describing the orientation of the triad of axes (A*) in the instants when less than three of said points (Pi) are visible to determine the attitude over time of said body ( 2 ) (step  108 ); 
 v. generating a white noise (step  109 ); 
 w. overlapping said white noise to said estimation of the quaternions (q*(tk)) referred to in the previous step  108  (step  110 ); 
 x. estimating the derivative ({dot over (q)}*(t k )) of the quaternions (q*(tk)) using a Kalman filter (step  111 ); 
 y. evaluating a first estimate of the angular velocity ({right arrow over (ω)}) of said body ( 2 ) depending on the derivative ({dot over (q)}*(t k )) (step  112 ); and 
 z. finally evaluating the angular velocity ({right arrow over (ω)}) of said body ( 2 ) through a filtering algorithm (step  113 ). 
 
     
     
         2 . A method according to  claim 1 , wherein said at least one remote sensor ( 1 ) is installed on board a spacecraft ( 3 ) in motion in an orbit close to that of said body ( 2 ). 
     
     
         3 . A method according to  claim 1 , wherein said at least one remote sensor ( 1 ) is housed in a earth station ( 5 ). 
     
     
         4 . A method according to  claim 2 , wherein the data acquired by said at least one remote sensor ( 1 ) are discontinuous due to the presence of non-visibility periods of at least one of said feature points (Pi) of said body ( 2 ). 
     
     
         5 . A method according to  claim 1 , wherein the geometrical configuration of said body ( 2 ) is known and, preferably, the relative position of said feature points (Pi) to be observed of said body ( 2 ) is known. 
     
     
         6 . A method according to  claim 1 , wherein the geometrical configuration of said body ( 2 ) is not known and the relative position of said feature points (Pi) to be observed of said body ( 2 ) is determined on the basis of the fact that, being known the coordinates of four different points in a time instant, their mutual positions, which are invariant, are determinable and of the fact that, when one of said feature points (Pi) is not visible in other time instants, its position can be identified by knowing that of said invariant mutual positions. 
     
     
         7 . A method according to  claim 1 , wherein the filtering algorithm used for the final evaluation of the angular velocity (ii) of said body ( 2 ) according to step m. (step  113 ) is based on the Basis Pursuit Denoising methodology by solving a minimum search problem, preferably by applying the SALSA algorithm. 
     
     
         8 . A system for measuring the angular velocity ({right arrow over (ω)}) of a body ( 2 ) orbiting in space, comprising:
 at least one remote sensor ( 1 ) for the acquisition of the data relevant to the positions taken over time (Pi(tk)) by a plurality (n) of feature points (Pi) to be observed of said body ( 2 ); 
 taking into account said plurality (n) of feature points (Pi), first means for the identification of 
 
       
         
           
             
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       triads of said points (Pi), which just as many triads (Aj) of axes correspond;
 second means for the identification of a triad of axes (Aj(tk)) associated to the first three points (Pu(tk),Pv(tk),Pw(tk) with u≠v≠w) available for each k th  instant; 
 third means for the evaluation, for each k th  instant, of the quaternions (qj(tk)) describing the orientation of the triad (Aj(tk)), associated to the triad (Pu(tk),Pv(tk),Pw(tk)), with respect to an inertial reference frame; 
 fourth means for the selection of a particular triad of axes (A*) and the evaluation of the quaternions (q*(tk)) describing its orientation with respect to said inertial reference frame depending on said quaternions (qj (tk)); 
 fifth means for the estimation of the quaternions (q*(tk)) describing the orientation of the triad of axes (A*) in the moments when less than three of said points (Pi) are visible to determine the attitude over time of said body ( 2 ); 
 sixth means for the generation of a white noise; 
 seventh means for the overlap of said white noise to said estimation of said quaternions (q*(tk)); 
 eighth means for the estimation of the derivative ({dot over (q)}*(t k )) of the quaternions (q*(tk)) using a Kalman filter; 
 ninth means for the evaluation of a first estimate of the angular velocity ({right arrow over (ω)}) of said body ( 2 ) depending on the derivative ({dot over (q)}*(t k )); and 
 tenth means for the final evaluation of the angular velocity ({right arrow over (ω)}) of said body ( 2 ) through a filtering algorithm. 
 
     
     
         9 . A system according to  claim 8 , wherein said at least one remote sensor ( 1 ) is installed on board a spacecraft ( 3 ). 
     
     
         10 . A system according to  claim 8 , wherein said at least one remote sensor ( 1 ) is housed in an earth station ( 5 ). 
     
     
         11 . A method according to  claim 3 , wherein the data acquired by said at least one remote sensor ( 1 ) are discontinuous due to the presence of non-visibility periods of at least one of said feature points (Pi) of said body ( 2 ).